Past exam of the condensed matter physics major option course of the University of Oxford / 2015 / 3 / c

Eu${}^{2+}$ has the half-filled $4f^7$ term with $L=0$. First-order orbital magnetism is therefore quenched already at the ion level, making the dominant moment approximately spin-only. Spin-orbit-induced magnetocrystalline anisotropy arises only through weaker admixtures and other small interactions; magnetic dipole interactions can also contribute. This explains why a cubic anisotropy term is allowed by symmetry but numerically weak.

An appropriate insulating local-moment model is a nearly isotropic Heisenberg model,with dominant effective ferromagnetic couplings in the sign convention $J_{ij}>0$. The Eu sublattice in rocksalt EuO is face-centered cubic; nearest- and further-neighbor effective exchanges can be retained as needed. Because the solid is not metallic, an itinerant-electron Stoner model or a generic free-carrier RKKY interaction mechanism is not the natural starting point. Exchange can still arise through virtual hopping and ligand-mediated processes in an insulator; it does not require mobile dc carriers.